Solve F=6x_{1}+10x_{2}rightarrowmax

$$F = 6 x _ { 1 } + 10 x _ { 2 } \rightarrow \max$$

Solve for x_1

$$x_{1}=\frac{F-10x_{2}}{6}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$6x_{1}+10x_{2}=F$$

Subtract 10x_{2} from both sides.

$$6x_{1}=F-10x_{2}$$

Divide both sides by 6.

$$\frac{6x_{1}}{6}=\frac{F-10x_{2}}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x_{1}=\frac{F-10x_{2}}{6}$$

Divide F-10x_{2} by 6.

$$x_{1}=\frac{F}{6}-\frac{5x_{2}}{3}$$

Solve for F

$$F=6x_{1}+10x_{2}$$